FEM vs analytic method - comparison

[Anonymous]

I made a comparison test of a console beam 25x25mm, 200 mm long, own weight loaded (gravity) and got suspicious results.

Please comment it and, if possible, explain why they are such as they are:

why FEM gives 23% higher stress in general?

why FEM with adaptive mesh refinement gives even 214% higher stress in critical points?

Max displacement is the same in all FEM cases and in analytic method, so these are only local error, but - how to avoid them and get precise result from FEM?
Where did I make mistakes?

Thanks in Advance

Model and FEM file:

https://a360.co/2oOVOZU

P.S. Why I can not rename Simulation Model 3 and 4 as I did for 1 and 2?

Calculation:

[TheCADWhisperer]

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@Anonymous wrote:

I made a comparison test of a console beam 25x25mm, 200 mm long, own weight...

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I haven't gone through your math yet or checked the model, but my first impression is 200mm test of gravity of that profile does not make a lot of sense to me.  

Also, can you post image of your problem similar to attachment (sorry, it is in inches, but I will convert to mm).

I am particularly concerned about load location as the typical book-problem is load (P in my image) applied at end of beam.  This is not the same as applying gravity.  Gravity load on a profile of that size and that short would be negligible.

We do this problem in my class every year and the hand calcs always match the analysis results.

I will try to show my example a bit later... ...check back.

[John_Holtz]

Hi @Anonymous 

The main reason the simulation results are higher is because of the mathematics of simulation: they do not work at corners and other regions of "singularities". See Hot spots (high stress) occur in a simulation. The high stress that I see in your models is limited to the corners and is a limitation of FEM. The adaptive mesh example that you referred to (not sure where that is in the model) demonstrates that the 4 points of highest stress are a singularity. You need to ignore those points and compare the average of the rest of the nodes to the hand calculations (which gives approximately 0.34 to 0.35 MPa in Simulation Model 4 Study 1 compared to 0.37 MPa hand calculations).

Another reason in general (but probably not in this case) is that the hand calculations make some simplifications, such as ignoring Poisson's Ratio, shear stresses, and so on.

Another reason may be that you are comparing the wrong results. The hand calculations are for the bending stress. In your model, that would be the Normal XX stress, not the von Mises stress.

P.S. The Simulation Models are renamed from within the Simplify environment. I was able to rename Simulation Model 3 by entering the Simplify environment, and then clicking the name to edit it.

[Anonymous]

I made comparison just to check if I do FEM right way - it is easy to check it analyticaly.

Take a look at screenshot attachment - it is one of FEM-solved cases.

Load location I applied is typical book-problem, too, but, of course, your are right - NOT the same as case with the load at the end of the beam.